Question

Starting from rest, a particle moving in a straight line has an acceleration of a=(2t−6) m/s2, where t is in seconds.

A. What is the particle's velocity when t = 7 s ?

Answer 1

To calculate the particle's velocity at t = 7 s, you integrate the acceleration function (2t−6) resulting in v(t) = t² - 6t. With an initial velocity of zero, at t = 7 s, the velocity is 7 m/s.

Step-by-step explanation:

The student asked what the particle's velocity would be at t = 7 s, given its acceleration is a=(2t−6) m/s², and it starts from rest. To find the velocity, we need to integrate the acceleration function with respect to time. We integrate (2t - 6) to get the velocity function v(t) = t² - 6t + C. Since the initial velocity is 0 (the particle starts from rest), the constant of integration C is 0. Thus, the velocity function simplifies to v(t) = t² - 6t. Plugging in t = 7 s gives v(7) = (7) ² - 6(7) = 49 - 42 = 7 m/s.